Incommensurate Ferroelectrics Research Articles

Ferroelectric incommensurate spin crystals.

Ferroics, especially ferromagnets, can form complex topological spin structures such as vortices1 and skyrmions2,3 when subjected to particular electrical and mechanical boundary conditions. Simple vortex-like, electric-dipole-based topological structures have been observed in dedicated ferroelectric systems, especially ferroelectric-insulator superlattices such as PbTiO3/SrTiO3, which was later shown to be a model system owing to its high depolarizing field4-8. To date, the electric dipole equivalent of ordered magnetic spin lattices driven by the Dzyaloshinskii-Moriya interaction (DMi)9,10 has not been experimentally observed. Here we examine a domain structure in a single PbTiO3 epitaxial layer sandwiched between SrRuO3 electrodes. We observe periodic clockwise and anticlockwise ferroelectric vortices that are modulated by a second ordering along their toroidal core. The resulting topology, supported by calculations, is a labyrinth-like pattern with two orthogonal periodic modulations that form an incommensurate polar crystal that provides a ferroelectric analogue to the recently discovered incommensurate spin crystals in ferromagnetic materials11-13. These findings further blur the border between emergent ferromagnetic and ferroelectric topologies, clearing the way for experimental realization of further electric counterparts of magnetic DMi-driven phases.

Impact of Mn3+ substitution on magnetization and electric polarization behavior in geometry frustrated CuFe1−xMnxO2

The Mn3+ doped single crystal samples CuFe1−xMnxO2 with x = 0.01, 0.03 and 0.05 were synthetic by floating zone method, and their magnetization and electric polarization were measured with static and pulsed high magnetic field up to 50 T in the temperature ranging from 2 to 300 K. A series of field-induced magnetic phase transitions and electric polarization, which show obviously anisotropy, were observed in all the doped samples, and their critical fields were directly related to the Mn3+ doping level. The pulsed high magnetic dielectric polarization measurements show that, in the ferroelectric incommensurate phase, the spontaneous electric polarization region is enhanced by the Mn3+ dopant. The impact of the Mn3+ substitution on magnetic and electric polarization behaviors may associate with the partial release of spin frustration in the CuFeO2. Based on the experimental results, the impact of Mn3+ doping on the magnetization and electric polarization behavior as well as their anisotropy are investigated and a detailed magnetic diagram are assumed.

Influence of nonmagnetic Ga ions on the magnetoelectric coupling in CuFe1−xGaxO2

The magnetic properties and dielectric polarization of CuFe1−xGaxO2 with various nonmagnetic Ga3+ doping levels have been measured in a wide magnetic field region, in which the observed experiment results have been explained by the consequence of the change in exchange interaction, dilution effect, and partial reduction of spin frustration. Compared with pure CuFeO2, doped nonmagnetic Ga3+ ions have an important effect on magnetization and polarization behavior and lead to an enhanced magnetoelectric coupling, especially, an enhanced spontaneous polarization has been observed in the doping amount of 0.02 and 0.05. This magnetoelectric effect appears mainly in the ferroelectric incommensurate magnetic phase region due to the noncollinear magnetic structure with a proper helical order in the CuFeO2. Based on the magnetization and polarization data, a magnetic phase diagram of temperature, magnetic field, and the doping amount are obtained.

Self-consistent theory of nanodomain formation on nonpolar surfaces of ferroelectrics

We propose a self-consistent theoretical approach capable of describing the features of the anisotropic nanodomain formation induced by a strongly inhomogeneous electric field of a charged scanning probe microscopy tip on nonpolar cuts of ferroelectrics. We obtained that a threshold field, previously regarded as an isotropic parameter, is an anisotropic function that is specified from the polar properties and lattice pinning anisotropy of a given ferroelectric in a self-consistent way. The proposed method for the calculation of the anisotropic threshold field is not material specific, thus the field should be anisotropic in all ferroelectrics with the spontaneous polarization anisotropy along the main crystallographic directions. The most evident examples are uniaxial ferroelectrics, layered ferroelectric perovskites, and low-symmetry incommensurate ferroelectrics. Obtained results quantitatively describe the differences at several times in the nanodomain length experimentally observed on $X$ and $Y$ cuts of $\mathrm{LiNb}{\mathrm{O}}_{3}$ and can give insight into the anisotropic dynamics of nanoscale polarization reversal in strongly inhomogeneous electric fields.

Mössbauer Spectroscopy of the Magnetic-Field-Induced Ferroelectric Phase of CuFeO2

57Fe Mossbauer spectroscopy in an applied magnetic field has been conducted on single crystals of CuFeO2 and CuFe0.965Ga0.035O2 in order to investigate magnetic-field-induced ferroelectric states. The Mossbauer spectra observed under a magnetic field change significantly, corresponding to magnetic-field-induced phase transitions. In the ferroelectric incommensurate (FEIC) phase (7 13 T) phases. In addition, a noticeable change in the hyperfine field is observed with varying magnetic field. We consider that these changes indicate the c...

Dielectric relaxation in a nonferroelectric phase of magneto-electric multiferroic CuFeO2

Magnetic oxide CuFeO2 is a rare magneto-electric multiferroic where magnetic field-induced or nonmagnetic impurity-induced proper helical magnetic ordering generates a spontaneous electric polarization. We have measured the complex permittivity in various magnetic phases under an applied magnetic field up to 15 T, and found distinct Debye-type-like dielectric dispersion with low relaxation frequency in only 4-sublattice (4SL) magnetic phase among various (4SL, ferroelectric incommensurate, 5-sublattice, partially disordered and paramagnetic) magnetic phases. The relaxation frequency of dielectric dispersion shows interesting anisotropic magnetic field dependence. As one possible explanation of this phenomenon, we will discuss the dielectric dispersion in terms of 4SL-specific magnetic domain wall motion and corresponding displacement of oxygen near magnetic domain wall, instead of so-called Maxwell-Wagner effect in the dielectric system with heterogeneous nature.

Ga-substitution-induced single ferroelectric phase in multiferroicCuFeO2

We have succeeded in realizing a single ferroelectric phase in ${\text{CuFe}}_{0.963}{\text{Ga}}_{0.037}{\text{O}}_{2}$ by substituting nonmagnetic ${\text{Ga}}^{3+}$ for ${\text{Fe}}^{3+}$ sites in ${\text{CuFeO}}_{2}$. Ferroelectric polarization $P$ in ${\text{CuFe}}_{0.963}{\text{Ga}}_{0.037}{\text{O}}_{2}$ is observed below 7.5 K, and has the relatively large value of $\ensuremath{\sim}250\text{ }\ensuremath{\mu}\text{C}/{\text{m}}^{2}$, which is comparable to $P=300\ensuremath{\sim}400\text{ }\ensuremath{\mu}\text{C}/{\text{m}}^{2}$ in the magnetic-field-induced ferroelectric phase of ${\text{CuFeO}}_{2}$. In neutron-diffraction measurements, a single magnetic diffraction peak with an incommensurate wave number was observed below 7.5 K in ${\text{CuFe}}_{0.963}{\text{Ga}}_{0.037}{\text{O}}_{2}$, indicating that the ferroelectric-incommensurate (FEIC) phase is realized as a single phase. Therefore, ${\text{CuFe}}_{0.963}{\text{Ga}}_{0.037}{\text{O}}_{2}$ with a single FEIC phase is strongly expected to provide the best opportunity to investigate unresolved problems regarding the ferroelectric mechanism in ${\text{CuFeO}}_{2}$. In this paper, we report measurements of magnetic susceptibility, specific heat, pyroelectric, dielectric constant, and neutron diffraction of a single crystal of ${\text{CuFe}}_{0.963}{\text{Ga}}_{0.037}{\text{O}}_{2}$.

Field-induced Incommensurate Lattice Modulations in the Delafossite CuFeO2

The results of synchrotron X-ray diffraction measurements on a single crystal of the triangular lattice antiferromagnet CuFeO 2 under zero and non-zero applied magnetic fields are reported. We find four satellite reflections at (0, 3+ q , 1/2), (0, 4- q , 1/2), (0, 4-2 q , 0), and (0, 3+2 q , 0) with the incommensurate wave number q ∼0.415 in the ferroelectric incommensurate (FEIC) phase which appears in the magnetic field, H , between 7 and 13 T at low temperatures. In the partially disordered (PD) phase which exists in the temperature, T , range between 11 and 14 K, we find two satellite reflections at (0, 4- q , 1/2) and (0, 4-2 q , 0) with the incommensurate wave number q ∼0.4. The T and H dependence of these satellite reflections are studied. We interpret that the reflections observed in the FEIC phase arise from incommensurate lattice modulations caused by a magnetoelastic coupling with the underlying magnetic structure. The observation of the reflection (0, 4- q , 1/2) in finite fields and the (0, ...

Transferred hyperfine field of Rb 2CoCl 4 single crystals in the ferroelectric–incommensurate–normal phase by 87Rb NMR

The molecular susceptibility and paramagnetic shift of Rb 2CoCl 4 single crystals grown using the slow evaporation method were measured, and from these experimental results we obtained the transferred hyperfine interaction due to the transfer of spin density from Co 2+ ions to Rb + ions. The transferred hyperfine field was obtained for the ferroelectric, incommensurate, and normal phases. In the case of Rb(I), the transferred hyperfine interaction decreases with increasing temperature in the incommensurate phase, and increases with increasing temperature in the normal phase. The value of H hf in the incommensurate and normal phases increases abruptly with increasing temperature in the case of Rb(II). These results indicate that the effects due to the transfer of spin density from Co 2+ ions to the Rb(I) and Rb(II) ions are large above T i. In particular, the effect due to the transfer of spin density to Rb(II) ions in the normal phase is very large; the variations with temperature of the transferred hyperfine interactions of the Rb(I) and Rb(II) nuclei are more or less continuous in T c1 and T i, and are not affected by the ferroelectric–incommensurate–normal phase transitions.

La-induced conversion between the ferroelectric and antiferroelectric incommensurate phases inPb1−xLax(Zr1−yTiy)O3

In La-substituted Pb 1 - x La x (Zr 0 . 9 5 Ti 0 . 0 5 )O 3 , an increase in the La content x served to convert the ferroelectric incommensurate (FI) phase into the antiferroelectric incommensurate (AI) phase around x=0.01. Inorder to elucidate the physical origin of the conversion between the FI and AI phases, the crystallographic features of the successive phase transitions related to these incommensurate phases have been investigated by transmission electron microscopy. It was found that the FI-to-AI transition actually occurred on cooling in the x =0.01 sample, and that in the x=0.03 sample, for instance, the AI phase basically consisted of four phases with commensurate modulations. The successive transitions among these four phases and the antiferroelectric commensurate (AC) phase were also suggested to proceed by the continuous change in a wave front of the modulation wave. In addition, the ferroelectric cluster (FS) state was found to exist in the paraelectric cubic (PC) phase above the AI phase. Because the M 3 and R 2 5 rotational displacements of the oxygen octahedra are, respectively, involved in the Fl phase and the FS state, the conversion between the FI and AI phases should be associated with that between these rotational displacements.

Roles of ferroelectricity, antiferroelectricity, and rotational displacement in the ferroelectric incommensurate phase ofPb(Zr1−xTix)O3

Crystallographic features of the ferroelectric incommensurate phase in $\mathrm{Pb}({\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{Ti}}_{x}){\mathrm{O}}_{3}$ have been investigated by transmission electron microscopy, mainly using $x=0.05$ samples obtained by cooling from a high-temperature paraelectric phase under an electric field of 500 V/cm. The present experimental data clearly indicate that the incommensurate and ferroelectric domains coexist independently, and that the incommensurate structure is characterized by not only a periodic-microdomain structure consisting of two ${M}_{3}$ variants, but also a periodic array of antiphase boundaries for the ${M}_{5}^{\ensuremath{'}}$ antiferroelectric displacement. These observations suggest that the normal structure of the incommensurate structure should be ferroelectric and that the rotational angle of the ${M}_{3}$ rotational displacement can be identified as a modulation mode. In addition, the antiphase boundary of the ${M}_{5}^{\ensuremath{'}}$ antiferroelectric displacement may play the role of discommensuration with a phase slip of \ensuremath{\pi}.

Modulated ferroelectrics

Modulated ferroelectrics represent a class of materials where the spontaneous polarization and/ or some other characteristic physical property varies in space in a regular manner. The presence of one or more modulation waves gives rise to a number of new phenomena which are not found in homogeneous ferroelectrics. Here we review the properties of:(a) incommensurate ferroelectrics with one, two or three independent modulation waves(b) ferroelectric and antiferroelectric liquid crystals in external fields and confined geometries where a crossover exists between a plane wave and a soliton-type modulation wave(c) composite and multiple layer type materials. The importance of some of these systems for applications will be also discussed.

Formation of an Amorphous Domain Pattern in Type-II Incommensurate Ferroelectrics

Coarsening of a domain pattern during the cooling process in type-II incommensurate ferroelectrics like NaNO 2 or thiourea is investigated in the framework of two-dimensional discrete lattice model derived from the Ishibashi-Shiba potential. The cooling process is simulated by gradual change of the parameters of potential with time. It has turned out that the resultant domain patterns differ depending on the cooling rate. The present lattice model can satisfactorily reproduce the formation of lamellar and amorphous domain patterns actually observed in NaNO 2 .

Low temperature properties of incommensurate ferroelectrics (PbySn1-y)2P2Se6

The complex dielectric susceptibility ϵ = ϵ′ + ϵ′′ of the incommensurate ferroelectrics (PbySn1-y)2P2Se6 (at y ≥0.4) has been studied at various frequencies (0.5 Hz – 100 kHz) in the temperature range from 10 mK to 200 K. Three different types of dielectric behaviour are distinguished at low temperature. Below 500mK typical glassy behaviour is observed according to the two-level system (TLS) model with a constant density of states. In the range from 0.5 K to 7 K the dielectric results are described in the TLS model with an energy dependent density of states and above 7 K the dielectric dispersion and associated maximum of ϵ′ has a thermoactivated relaxation nature. The latter is attributed to the freezing of the relaxation dynamics of the incommensurate modulation.

NMR in multiple-q modulated incommensurate and helicoidal ferroelectrics

Abstract The application of NMR and NQR for the study of local properties of multiple-q modulated incommensurate ferroelectrics and helicoidal ferroelectrics is reviewed and some recent advances in this field are described.

Raman scattering on acoustic and soft modes in incommensurate ferroelectric thiourea

Abstract Lattice dynamics of incommensurate ferroelectrics thiourea are investigated both theoretically and experimentally. Intermolecular interactions parameters are shown to change considerably during paraelectric-incommensurate (P-I) and incommensurate-ferroelectric (I-F) phase transitions. Acoustic modes activation and strong interaction of one of them with the soft lattice mode are observed in the I phase.

Critical Behaviour of Specific Heat in Ferroelectric K2ZnCl4and (NH4)2BeF4at Normal-Incommensurate Phase Transition

Measurements of specific heat were carried out on structurally incommensurate ferroelectrics K 2 ZnCl 4 and (NH 4 ) 2 BeF 4 over a wide temperature region with an AC calorimetric technique. Critical indices α associated with the normal-incommensurate phase transition are obtained as 0.12±0.02 for K 2 ZnCl 4 and 0.18±0.02 for (NH 4 ) 2 BeF 4 . These values do not agree with that in the 3 d XY-model proposed by Bruce and Cowley, and are rather comparable with α=0.125 for the 3 d Ising-model. A crossover from a logarithmic behaviour to a power-law behaviour was found at reduced temperatures t cr =1×10 -3 for K 2 ZnCl 4 and 5×10 -3 for (NH 4 ) 2 BeF 4 , respectively.

Transitions to Simultaneously Incommensurateand Ferroelectric Phases When the Numberof (Proper) Order Parameters Is One

Transitions from prototypic phases to simultaneously incommensurate and ferroelectric phases are possible even when the number of (proper) order parameters is one. A case is investigated where the prototype point group is mmm and the (proper) order parameter belongs to the zero-wavenumber irreducible representation, B 2 u . A subsidiary order parameter, which is not soft like the proper one but moderately hard, is taken into account; it belongs to B 1 u . The B 2 u and B 1 u order parameters can be identified with polarization components P y and P z respectively. The free energy function contains term P y ( P z ∂ z P y - P y ∂ z P z ). This term can generate a phase incommensurate in the z direction and ferroelectric in the y direction. Sufficient conditions are found out for this ferroelectric incommensurate phase to outrival other ferroic phases in succeeding the prototypic phase.

NMR In Disordered ferroelectrics and deuteron glasses

Conventional methods of crystal structure determination yield the unit cell structure averaged over space and time. Here we review three different types of fundamental NMR experiments which allow for the determination of the local atomic structure in: i) incommensurate ferroelectrics, ii) hydrogenbonded order-disorder-type ferroelectrics, iii) deuteron glasses.It is shown that NMR can be used to determine the soliton density in incommensurate systems and allows for a direct observation of the intra H-bond proton and deuteron motion. It also allows for the determination of the Edwards-Anderson order parameter in glasses.

Temperature Dependences of Linear Electro-Incommensurate Constants in the Vicinity of the Transition from a Prototypic Phase to a Simultaneously Incommensurate and Ferroelectric Phase

The material constants that characterize simultaneously incommensurate and ferroelectric phases are linear electro-incommensurate constants, such as d h /d E , d q 1 /d E and d q n /d E , where E denotes an electric field applied in the direction of spontaneous polarization, h the wavenumber of the first harmonic (the fundamental wave) in Q (any one of the order parameters), q 1 the amplitude of the first harmonic, and q n the amplitude of the n th harmonic (a high harmonic). One typical case is investigated, namely the P \bar4 b 2-(1/2, 0, 0) case. In this case, a ferroelectric incommensurate phase of the absolute type is possible. The transition between this phase and the prototypic phase can be second order. The expressions of the temperature dependences of almost all linear electro-incommensurate constants in the vicinity of the mentioned transition are presented.